OFFSET
1,1
COMMENTS
Using empirical data for 1 <= k <= 10000, it has been found that the distribution of these terms correlates well (R^2 = 0.9513) with f(k) = c*k^(1/2) with c approximately 0.73. In addition, f'(k) approximates the probability that any particular k has this property. Any terms in A056154 must also be in this sequence.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..200
EXAMPLE
First term: 2^2 = 11_3, 2^3 = 22_3, both with 0 zeros and both of length 2.
Second term: 2^5 = 1012_3, 2^6 = 2101_3, both with 1 zero and both of length 4.
MATHEMATICA
Select[Range[4200], IntegerLength[2^#, 3]==IntegerLength[2^(#+1), 3] && DigitCount[ 2^#, 3, 0]==DigitCount[2^(#+1), 3, 0]&] (* Harvey P. Dale, Dec 10 2021 *)
PROG
(PARI) isok(k) = my(da=digits(2^k, 3), db=digits(2^(k+1), 3)); (#da == #db) && (#select(x->(x==0), da) == #select(x->(x==0), db)); \\ Michel Marcus, Jul 01 2021
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Russell Harper (rharper(AT)intouchsurvey.com), Aug 13 2000
STATUS
approved